Question

The height and radius of a cylinder are equal, An error of 2 % is made in measuring height.The approximate percentage error in volume is .......,Select correct option from the given options.
(a) 6%
(b) 4%
(c) 3%
(d) 2%

Answer 1

error is power of the question multiplied by the error given...
I.e. a. 6%

Answer 2

answer : option (a) 6%

explanation : the height and radius of cylinder are equal, an error of 2% is made in measuring height. so, it's clear error in measuring radius is also 2% .

volume of cylinder , V = πr²h

taking log both sides ,

logV = log(πr²h)

logV = log(π) + 2log(r) + log(h)

differentiating both sides,

dV/V = 0 + 2 dr/r + dh/h

or, ∆V/V = 2 ∆r/r + ∆h/h

or, % error in volume = 2 × % error in r + % error in h

= 2 × 2% + 2 %

= 6 %

hence, error in volume of cylinder is 6%